A small ball of mass 2.00 kilograms is moving at a velocity 1.50 meters/second. It hits a larger, stationary ball of mass 5.00 kilograms. What is the kinetic energy of the system after the collision if the collision is elastic?

Well, the situation seems quite "ball-istic"! Let's dive into the problem.

In an elastic collision, the total kinetic energy of the system is conserved. So, we need to calculate the initial and final kinetic energy of both balls.

The initial kinetic energy of the small ball can be calculated using the formula:

Kinetic Energy = (1/2) * mass * velocity^2

So, for the small ball:
Kinetic Energy(initial) = (1/2) * 2.00 kg * (1.50 m/s)^2

Calculating that, we get:
Kinetic Energy(initial) = 2.25 Joules

Since the larger ball is stationary, its initial kinetic energy is zero.

Now, let's find the final kinetic energy. Since we know the collision is elastic, the total kinetic energy of the system remains conserved.

So, the final kinetic energy will be the sum of the kinetic energies of both balls after the collision.

For the small ball:
Kinetic Energy(small ball) = (1/2) * 2.00 kg * velocity^2

And for the larger ball:
Kinetic Energy(large ball) = (1/2) * 5.00 kg * 0^2 (because it is stationary, its velocity is zero)

Simplifying that, we have:
Kinetic Energy(large ball) = 0 Joules

Now, adding the two kinetic energies together, we get the final kinetic energy:

Kinetic Energy(final) = Kinetic Energy(small ball) + Kinetic Energy(large ball)

Plugging in the values, we get:
Kinetic Energy(final) = 2.25 Joules + 0 Joules

So, after the collision, if it is elastic, the kinetic energy of the system will remain 2.25 Joules.

Remember, kids, laughter is kinetic energy for the soul!

To find the kinetic energy of a system after an elastic collision, we need to apply the law of conservation of kinetic energy which states that the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

First, let's calculate the initial kinetic energy before the collision for both balls separately:
Kinetic energy of the small ball (K1) = (1/2) * mass1 * velocity1^2
= (1/2) * 2.00 kg * (1.50 m/s)^2

Kinetic energy of the large ball (K2) = (1/2) * mass2 * velocity2^2
= (1/2) * 5.00 kg * (0 m/s)^2 [since the large ball is stationary]

Since the large ball is stationary, its initial kinetic energy (K2) will be zero.

Now, let's find the total initial kinetic energy:
Initial kinetic energy (K_initial) = K1 + K2

Next, since the collision is elastic, the total kinetic energy after the collision will be the same as the initial kinetic energy:
Total kinetic energy after collision (K_final) = K_initial

Therefore, the kinetic energy of the system after the collision is equal to the initial kinetic energy, which is given by:
K_final = K_initial

Now, let's substitute the values and calculate the answer:

To find the kinetic energy of the system after the collision, we first need to calculate the initial kinetic energy of both balls separately, before the collision. The kinetic energy of an object can be calculated using the formula:

Kinetic energy = (1/2) * mass * velocity^2

For the small ball:
Mass of the small ball = 2.00 kilograms
Velocity of the small ball = 1.50 meters/second

Using the formula, the initial kinetic energy of the small ball is:
Kinetic energy = (1/2) * 2.00 kg * (1.50 m/s)^2
Kinetic energy = 1/2 * 2.00 kg * 2.25 m^2/s^2
Kinetic energy = 2.25 Joules

For the larger ball:
Mass of the larger ball = 5.00 kilograms
Velocity of the larger ball = 0 meters/second (since it is stationary)

Using the formula, the initial kinetic energy of the larger ball is:
Kinetic energy = (1/2) * 5.00 kg * (0 m/s)^2
Kinetic energy = 0 Joules

Now, for an elastic collision, the total kinetic energy before and after the collision remains the same. Therefore, the sum of the initial kinetic energy of both balls will be equal to the sum of the final kinetic energy of both balls.

Initial kinetic energy of system = 2.25 Joules + 0 Joules
Initial kinetic energy of system = 2.25 Joules

Therefore, the kinetic energy of the system after the elastic collision is also 2.25 Joules.

if energy is conserved, KE after=KE before

KE after=1/2 m v^2=.001 *1.5^2 Joules